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Isomorphism of all natural languages
Day nine -- Question -- from "Trailsend" -- Let A and B be the respective sets of lexemes of two distinct languages. Let X be a universal language as described in i, and let X(Y) be the "encoding" of the set Y in X. There ought to also be some inverses of X(Y), X_N(x), which map some set encoded in X back to a natural language N. For criterion i to hold, X_A(X(B)) = A, X_B(X(A)) = B, etc. Thus, X_A(X(X_B(X(A)))) = A, and so on and so forth. (That is, the transform X can map from A to B and back any number of times, while the mapping is preserved.) This can only hold, however, if the sets A and B are isomorphic. Otherwise, they will have different structural patterns, and it will be impossible to use a single transform to bidirectionally map between the two. As I (and others) have mentioned earlier, this is a fatal flaw of the theory, not just of the application. All the thousands of languages in the world are nowhere close to isomorphic, and therefore require a great number of "transforms" to map from one to the other. Your system may certainly work for "encoding" Chinese into English, because it was built on Chinese with English in mind. But there is no evidence that it will also be able to fully map Hindi to Nahuatl, for example. Answer -- This is truly a very good and very important issue. Indeed, you are right. For criterion i to hold, set A and set B must be isomorphic. The definition of "isomorphic" in mathematics uses a lot of math jargons. At here, we say that if two sets can find one to one correspondence to all their members, then those sets are isomorphic to each other. This is not a precise mathematic definition but is good enough for our purpose here. For the "fact" that we can always make translations between two languages, to and back, is already "a kind of" proof that those two language sets are isomorphic, although we might need to use a few different pathways to translate them, such as: 1. Formal translation -- word to word 2. Semantic translation -- meaning to meaning 3. Phonetic translation -- phonetic importing, such Kung-fu 4. Note tag translation -- must include a note to explain the translation As this issue is so important, I will discuss it in better details as follow: 1. Instead of comparing member to member, we can compare the structure of the two sets. That is, listing the necessary and the sufficient conditions for each set, and they can be compared. In the main page of the prebabel site, I did such a list (especially for English), and it could be a partial answer for this question. A better description of the necessary and the sufficient conditions for "any" language was described in detail in a paper written in June 2007 (35 pages), and it is available at http://www.chinese-word-roots.org/cwr018.htm 2. The "Private Language Thesis (PLT)" -- is a private language possible? This is an issue discussed both in detail and in depth in philosophy of language. The PLT states that "any private language is impossible." I will not repeat their discussions and reasonings here, as it is too much to talk about and the kind of language that they were using having too many jargons. Yet, I will make some my own observations here. 1. If a private language is possible in one language, then by definition, that part (the private part) of that language can never be translated to any other language. Thus, that language can never be isomorphic to any other language. Yet, for a practical purpose, we can remove that private part from that language, and the remainder of that language becomes isomorphic to other languages. Then, all languages are still isomorphic among one another practically, although not theoretically. 2. I, personally, do agree with the PLT that any private language (including the Martian, if any) is impossible under any circumstances. As a theorist on theoretical physics, I do know that there is still a small spot of the universe which is unknown to physics. That is, the language that used by that small spot or that is needed to describe that small spot is private in all senses, practically and theoretically. But, all physicists are all confident that we can understand any private languages of nature as soon as we can "hear" it, such as by using some detectors. Our biggest problem is that we cannot hear those private languages with our senses. During the past 10 years, over 10 billion US dollars were spent to build a Large Hadron Colliders (with the most advanced detectors, the eyes and the ears). As soon as that private language of the sub-particle world is heard, we, physicists, will be able to decode it. Maybe someone will say that God's language is incomprehensible to human and is, thus, private. Well, I won't argue with that but will exclude it from the PLT which encompasses only the non-God languages. Maybe someone will say that many dead languages are private. Well, a dead language is no long a language, as there is no longer a conversation between it to us, although many dead languages can still be decoded. Any dead language is not an issue for PLT. With these and with the fact that all known natural languages can "always" be translated among one another, the proof of isomorphic among all languages can be worked out theoretically in mathematics. I did discuss four theorems before and will add one "Isomorphic theorem" here. I am listing them below again. 1. Isomorphic theorem -- All natural languages are isomorphic among one another regardless of how huge a difference between their looks superficially, such as Chinese and English both on their word symbols and the grammar. 2. Existence theorem -- There is, at list, one (1) 100% axiomatized set R (root word set) which is able to encode one natural language. 3. Universal theorem -- If Set R can encode one natural language L1, then Set R can encode all other natural languages. The Set R is called the PreBabel set. 4. Uniqueness theorem -- If Set R1 and Set R2 are both PreBabel sets, R1 and R2 are isomorphic. 5. Fuzziness theorem -- If Set R is a PreBabel set, then Set R must be a fuzzy set. Those theorems can be proved mathematically even without an actual Set R "on Hand." However, everything changes as soon as an actual Set R is "on" hand. Those theorems are no longer just provable theoretically but are "testable" physically and practically. 1. The current PB set is able to encode the traditional Chinese character set completely, 100%. This is testable, simply check out every Chinese character with the PB set. 2. Using the current PB set to encode any other natural language, such as English. I did about 300 English words. This is, indeed, a testable procedure. 3. As the Chinese system is already 100% encoded, the criteria ii and iii "becomes" testable (no longer theoretical). And, I discussed this in my last post. Of course, I have not covered all issues about a universal language. However, the above outline does provide a clear framework for a universal language. Many of your critiques are truly good, such as: 1. Why are there "bird's head" and "bird's head in general"? 2. Any universal language will eventually diverge,... 3. Semantics 4. ... I will discuss these issues soon. Signature -- PreBabel is the true universal language, it is available at http://www.prebabel.info